Least Common Multiple (LCM) of 67 and 156
The least common multiple (LCM) of 67 and 156 is 10452.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 67 and 156?
First, calculate the GCD of 67 and 156 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 156 = 0 remainder 67 |
| 2 | 156 ÷ 67 = 2 remainder 22 |
| 3 | 67 ÷ 22 = 3 remainder 1 |
| 4 | 22 ÷ 1 = 22 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 66 and 198 | 198 |
| 144 and 11 | 1584 |
| 167 and 48 | 8016 |
| 112 and 118 | 6608 |
| 81 and 77 | 6237 |